The most common negative prefixes in English are in-, un-, non-, de-, dis-, a-, anti-, im-, il-, and ir-. Words that take il– as a negative prefix always begin with the letter l: logical - illogical.

You should always use "illogical." "Unlogical" is not a word in English.

Is it native speakers can understand me with a word Unlogical?

Further to Georges comment, you should be aware that there is such a word as UNlogical that is related to illogical, but is distinct from it. UNlogical= adjective lacking in correct logical relation. Which is as described by George. The teachers who have answered from an English teachers grammar only perspective have not fully addressed your question. No you cannot use illogical and UNlogical in the same ways. For an email about most subjects you could and would say illogical, but if sending an email about a scientific subject like physics, you can legitimately say something like the sine waves on the graphs are acting Unlogically, although Illogical that word could also be used. Unlogical was used in the past in many writings. Appears to be no longer in vogue. Spellcheckers today will not automatically accept "UNlogical".

ILLOGICAL is the opposite of logical, but UNLOGICAL is distinct from logical. An example is a triangle, in logical mathematics the sum of the 3 angles equal 180degrees. It is illogical when somebody assigns the internal angles to a triangle 100, 100 and 100 degrees. But, if you started from the North Pole, walked 100m, turned 90degrees right then walked for 100m then turned 90degrees right and walk 100m you have walked an Unlogical triangle with 270degrees.